$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 5x + 9$ and $ JT = 6x + 3$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {5x + 9} = {6x + 3}$ Solve for $x$ $ -x = -6$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 5({6}) + 9$ $ JT = 6({6}) + 3$ $ CJ = 30 + 9$ $ JT = 36 + 3$ $ CJ = 39$ $ JT = 39$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {39} + {39}$ $ CT = 78$